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 Is there a Sturmian theory

主讲人：Peter Bates

摘要：For a given dynamical system, and a given real-valued function, the field of Ergodic Optimization seeks to understand those orbits (or invariant measures) that realise the largest possible ergodic average. Rather often, these orbits turn out to be in some sense `simple', for example periodic, or non-periodic but of low complexity (e.g. Sturmian). Ergodic dominance is one strategy, appealing to ideas from stochastic dominance, for understanding the optimizing orbits and measures for certain classes of functions. One application is to constrained optimization problems for digit expansions: e.g. if we fix the mean value of the decimal digits of a number, or equivalently fix the arithmetic mean of an orbit under the map x-> 10x (mod 1), how can we minimize the variance around the mean, and how can we maximize the geometric mean?

主讲人简介：Peter Bates，Michigan State University数学系教授.

邀请人：李骥

时间：2024年6月2日（星期六）10:30-12:00

地点：科技楼南楼706室